Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/non-Hamiltonian.In this paper a computational complexity theory of the “knowledge” contained in a proof is developed. Zero-knowledge proofs are defined as those proofs that convey no additional knowledge other than the correctness of the proposition in question. Examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity. These are the first examples of zero-knowledge proofs for languages not known to be efficiently recognizable.

/pdf/the-knowledge-complexity-of-interactive-proof-systems-31apre0ecf.pdf

The knowledge complexity of interactive proof-systems

Concurrent executions of a zero-knowledge protocol by a single prover (with one or more verifiers) may leak information and may not be zero-knowledge in toto. In this article, we study the problem of maintaining zero-knowledge.We introduce the notion of an (α, β) timing constraint: for any two processors P1 and P2, if P1 measures α elapsed time on its local clock and P2 measures β elapsed time on its local clock, and P2 starts afterP1 does, then P2 will finish after P1 does. We show that if the adversary is constrained by an (α, β) assumption then there exist four-round almost concurrent zero-knowledge interactive proofs and perfect concurrent zero-knowledge arguments for every language in NP. We also address the more specific problem of Deniable Authentication, for which we propose several particularly efficient solutions. Deniable Authentication is of independent interest, even in the sequential case; our concurrent solutions yield sequential solutions without recourse to timing, that is, in the standard model.

Concurrent Zero-Knowledge.

The concept of group signatures allows a group member to sign messages anonymously on behalf of the group However, in the case of a dispute, the identity of a signature's originator can be revealed by a designated entity In this paper we propose a new group signature scheme that is well suited for large groups, ie, the length of the group's public key and of signatures do not depend on the size of the group Our solution based on a variation of the RSA problem is more efficient than previous ones satisfying these requirements

A group signature scheme with improved efficiency

The group signatures allow any member to sign the message on behalf of the group. While anyone who does not need to be a group member can verify the signature, they do not know who the signer is. The first examples are constructed using classical techniques such as the discrete logarithm and the integer factorization problem. The fact that the cryptosystems using classical techniques will be broken in polynomial time with quantum computing power increases the interest in post-quantum cryptography. Lattice-based cryptography is a good alternative for the post-quantum world due to its simple structures, efficient implementations, and worst-case hardness. Therefore, the lattice-based group signature schemes have been proposed for quantum era. In this paper, our aim is to review group signature schemes over lattices. We classify the schemes into four groups according to the fact that they allow adding and revoking members: static, group signature schemes with revocation mechanism, partially dynamic and fully dynamic. Firstly, we define the algorithms needed to construct the schemes. We give the development process and requirements for constructing group signatures before we review all group signature schemes over lattices. In addition, we compare all proposed lattice-based group signature schemes in view of underlying lattice problems, security requirements, the sizes of group public and secret signing key, signature size and security model. The main contribution of this study is that it is the first study examining lattice-based group signature schemes in detail. 

A survey of quantum secure group signature schemes: Lattice-based approach

Message-dependent opening is one of the solutions to solve the problem of the tracing manager owns excessive power. In this paper, we present a new lattice-based fully dynamic group signature scheme with message-dependent opening by combining an improved version of the fully dynamic group signature scheme proposed by Ling et al and the double encryption paradigm. In addition, we propose an improved underlying zero knowledge protocol, it has a soundness error $\frac {1}{\max (n,p)+1}$
 that is better than the Stern-like protocol, which helps to bring down the communication complexity of the protocol and hence the signature scheme. Our scheme constrains the power of group managers by adding an admitter, and the signature size has a logarithmic relationship with the group size.

/pdf/an-efficient-fully-dynamic-group-signature-with-message-4clxk72f80.pdf

An efficient fully dynamic group signature with message dependent opening from lattice

The group signature scheme is an important primitive in cryptography, it allows members in a group to generate signatures anonymously on behalf of the whole group. In view of the practical application of such schemes, it is necessary to allow users’ registration and revocation when necessary, which makes the construction of dynamic group signature schemes become a significant direction. On the basis of (Ling et al., Lattice-based group signatures: achieving full dynamicity with ease, 2017), we present the first full dynamic group signature scheme over ring, and under the premise of ensuring security, the efficiency of the scheme is improved mainly from the following three aspects: the size of keys, the dynamic construction of a Merkle hash tree that used to record the information of registered users, and the reuse of the leaves in this tree. In addition, the public and secret keys of both group manager and trace manager are generated by a trusted third party, which prevents the situation that the two managers generate their respective public key and secret key maliciously. Compared with the counterpart of the scheme in (Ling et al., Lattice-based group signatures: achieving full dynamicity with ease, 2017) over ring, the expected space complexity of the Merkle tree used in our work down almost by half, and the computational complexity of its update has been reduced by a notch because of the dynamic construction of the hash tree.

/pdf/an-efficient-full-dynamic-group-signature-scheme-over-ring-nx9ehvzh2s.pdf

An efficient full dynamic group signature scheme over ring

Concurrent non-malleable zero-knowledge (CNMZK) considers the concurrent execution of zero-knowledge protocols in a setting even when adversaries can simultaneously corrupt multiple provers and verifiers. As far as we know, the round complexity of all the constructions of CNMZK arguments for NP is at least ω(logn). In this paper, we provide the first construction of a constant-round concurrent non-malleable zero-knowledge argument for every language in NP. Our protocol relies on the existence of families of collision-resistant hash functions, one-way permutations and indistinguishability obfuscators. As an additional contribution, we study the composition of two central notions in zero knowledge, the simultaneously resettable zero-knowledge and non-malleable zero-knowledge, which seemingly have stronger proved security guarantees. We give the first construction of a constant-round simultaneously-resettable non-malleable zero-knowledge. To the best of our knowledge, this is the first study to combine the two security concepts described above together in the zero-knowledge protocols.

/pdf/concurrent-non-malleable-zero-knowledge-and-simultaneous-4fu0krwwgx.pdf

Concurrent non-malleable zero-knowledge and simultaneous resettable non-malleable zero-knowledge in constant rounds

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An efficient full dynamic group signature scheme over ring

An efficient fully dynamic group signature with message dependent opening from lattice

Concurrent non-malleable zero-knowledge and simultaneous resettable non-malleable zero-knowledge in constant rounds